Abstract

Ultra-intense single attosecond pulse (AP) can be obtained from circularly polarized (CP) laser interacting with overdense plasma. High harmonics are naturally generated in the reflected laser pulses due to the laser-induced one-time drastic oscillation of the plasma boundary. Using two-dimensional (2D) planar particle-in-cell (PIC) simulations and analytical model, we show that multi-dimensional effects have great influence on the generation of AP. Self-focusing and defocusing phenomena occur in front of the compressed plasma boundary, which lead to the dispersion of the generated AP in the far field. We propose to control the reflected high harmonics by employing a density-modulated foil target (DMFT). When the target density distribution fits the laser intensity profile, the intensity of the attosecond pulse generated from the center part of the plasma has a flatten profile within the center range in the transverse direction. It is shown that a single 300 attosecond (1 as = 10−18 s) pulse with the intensity of 1.4 × 1021 W cm−2 can be naturally generated. Further simulations reveal that the reflected high harmonics properties are highly related to the modulated density distribution and the phase offset between laser field and the carrier envelope. The emission direction of the AP generated from the plasma boundary can be controlled in a very wide range in front of the plasma surface by combining the DMFT and a suitable driving laser.

© 2013 Optical Society of America

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    [CrossRef]
  20. N. M. Naumova, J. A. Nees, B. Hou, G. A. Mourou, and I. V. Sokolov, “Isolated attosecond pulses generated by relativistic effects in a wavelength-cubedfocal volume,” Opt. Lett.29, 778–780 (2004).
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    [CrossRef]
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    [CrossRef]
  24. T. Yu, M. Chen, and A. Pukhov, “High quality gev proton beams from a density-modulated foil target,” Laser Part. Beams27, 611–617 (2009).
    [CrossRef]
  25. M. Chen, A. Pukhov, T. P. Yu, and Z. M. Sheng, “Enhanced collimated gev monoenergetic ion acceleration from a shaped foil target irradiated by a circularly polarized laser pulse,” Phys. Rev. Lett.103, 024801 (2009).
    [CrossRef] [PubMed]
  26. A. Macchi, F. Cattani, T. V. Liseykina, and F. Cornolti, “Laser acceleration of ion bunches at the front surface of overdense plasmas,” Phys. Rev. Lett.94, 165003 (2005).
    [CrossRef] [PubMed]
  27. S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, “Coherent focusing of high harmonics: A new way towards the extreme intensities,” Phys. Rev. Lett.94, 103903 (2005).
    [CrossRef] [PubMed]
  28. C. Nieter and J. R. Cary, “Vorpal: a versatile plasma simulation code,” J. Comput. Phys.196, 448–473 (2004).
    [CrossRef]
  29. S. C. Wilks, W. L. Kruer, M. Tabak, and A. B. Langdon, “Absorption of ultra-intense laser pulses,” Phys. Rev. Lett.69, 1383–1386 (1992).
    [CrossRef] [PubMed]
  30. M. Chen, A. Pukhov, Z. M. Sheng, and X. Q. Yan, “Laser mode effects on the ion acceleration during circularly polarized laser pulse interaction with foil targets,” Phys. Plasmas15, 113103 (2008).
    [CrossRef]
  31. X. Q. Yan, H. C. Wu, Z. M. Sheng, J. E. Chen, and J. Meyer-ter Vehn, “Self-organizing gev, nanocoulomb, collimated proton beam from laser foil interaction at 7 × 1021W/cm2,” Phys. Rev. Lett.103, 135001 (2009).
    [CrossRef]
  32. D. an der Brügge and A. Pukhov, “Propagation of relativistic surface harmonics radiation in free space,” Phys. Plasmas14, 093104 (2007).
    [CrossRef]
  33. A. Pukhov, T. Baeva, and D. an der Brgge, “Relativistic laser plasmas for novel radiation sources,” Eur. Phys. J. Spec. Top.175, 25–33 (2009).
    [CrossRef]
  34. S. Gordienko and A. Pukhov, “Scalings for ultrarelativistic laser plasmas and quasimonoenergetic electrons,” Phys. Plasmas12, 043109 (2005).
    [CrossRef]
  35. X. Lavocat-Dubuis, F. Vidal, J.-P. Matte, J.-C. Kieffer, and T. Ozaki, “Multiple attosecond pulse generation in relativistically laser-driven overdense plasmas,” New J. Phys.13, 023039 (2011).
    [CrossRef]
  36. L. L. Ji, B. F. Shen, D. X. Li, D. Wang, Y. X. Leng, X. M. Zhang, M. Wen, W. P. Wang, J. C. Xu, and Y. H. Yu., “Relativistic single-cycled short-wavelength laser pulse compressed from a chirped pulse induced by laser-foil interaction,” Phys. Rev. Lett.105, 025001 (2010).
    [CrossRef] [PubMed]
  37. M. Geissler, S. Rykovanov, J. Schreiber, J. M. ter Vehn, and G. D. Tsakiris, “3d simulations of surface harmonic generation with few-cycle laser pulses,” New J. Phys.9, 218 (2007).
    [CrossRef]
  38. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys.70, 1–87 (2007).
    [CrossRef]
  39. D. an der Brügge, N. Kumar, A. Pukhov, and C. Rödel, “Influence of surface waves on plasma high-order harmonic generation,” Phys. Rev. Lett.108, 125002 (2012).
    [CrossRef] [PubMed]
  40. T.-P. Yu, A. Pukhov, G. Shvets, and M. Chen, “Stable laser-driven proton beam acceleration from a two-ion-species ultrathin foil,” Phys. Rev. Lett.105, 065002 (2010).
    [CrossRef] [PubMed]
  41. T. Esirkepov, M. Borghesi, S. V. Bulanov, G. Mourou, and T. Tajima, “Highly efficient relativistic-ion generation in the laser-piston regime,” Phys. Rev. Lett.92, 175003 (2004).
    [CrossRef] [PubMed]
  42. L. L. Ji, B. F. Shen, X. M. Zhang, F. C. Wang, Z. Y. Jin, C. Q. Xia, M. Wen, W. P. Wang, J. C. Xu, and M. Y. Yu, “Generating quasi-single-cycle relativistic laser pulses by laser-foil interaction,” Phys. Rev. Lett.103, 215005 (2009).
    [CrossRef]
  43. G. D. Tsakiris, K. Eidmann, J. M. ter Vehn, and F. Krausz, “Route to intense single attosecond pulses,” New J. Phys.8, 19 (2006).
    [CrossRef]
  44. J. Zheng, Z.-M. Sheng, J. Zhang, M. Chen, and Y.-Y. Ma, “Effects of laser intensities and target shapes on attosecond pulse generation from irradiated solid surfaces,” Chin. Phys. Lett.23, 377–380 (2006).
    [CrossRef]

2013 (1)

T.-P. Yu, A. Pukhov, Z.-M. Sheng, F. Liu, and G. Shvets, “Bright betatronlike x rays from radiation pressure acceleration of a mass-limited foil target,” Phys. Rev. Lett.110, 045001 (2013).
[CrossRef]

2012 (3)

H.-C. Wu and J. Meyer-ter Vehn, “Giant half-cycle attosecond pulses,” Nature Photon.6, 304–307 (2012).
[CrossRef]

J. Liangliang, S. Baifei, Z. Xiaomei, W. Wenpeng, Y. Yahong, W. Xiaofeng, Y. Longqing, and S. Yin, “Plasma approach for generating ultra-intense single attosecond pulse,” Plasma Sci. Technol.14, 859–863 (2012).
[CrossRef]

D. an der Brügge, N. Kumar, A. Pukhov, and C. Rödel, “Influence of surface waves on plasma high-order harmonic generation,” Phys. Rev. Lett.108, 125002 (2012).
[CrossRef] [PubMed]

2011 (2)

L. Ji, B. Shen, X. Zhang, M. Wen, C. Xia, W. Wang, J. Xu, Y. Yu, M. Yu, and Z. Xu, “Ultra-intense single attosecond pulse generated from circularly polarized laser interacting with overdense plasma,” Phys. Plasmas18, 083104 (2011).
[CrossRef]

X. Lavocat-Dubuis, F. Vidal, J.-P. Matte, J.-C. Kieffer, and T. Ozaki, “Multiple attosecond pulse generation in relativistically laser-driven overdense plasmas,” New J. Phys.13, 023039 (2011).
[CrossRef]

2010 (3)

L. L. Ji, B. F. Shen, D. X. Li, D. Wang, Y. X. Leng, X. M. Zhang, M. Wen, W. P. Wang, J. C. Xu, and Y. H. Yu., “Relativistic single-cycled short-wavelength laser pulse compressed from a chirped pulse induced by laser-foil interaction,” Phys. Rev. Lett.105, 025001 (2010).
[CrossRef] [PubMed]

C. Thaury and F. Quéré, “High-order harmonic and attosecond pulse generation on plasma mirrors: basic mechanisms,” J. Phys. B: At. Mol. Opt. Phys.43, 213001 (2010).
[CrossRef]

T.-P. Yu, A. Pukhov, G. Shvets, and M. Chen, “Stable laser-driven proton beam acceleration from a two-ion-species ultrathin foil,” Phys. Rev. Lett.105, 065002 (2010).
[CrossRef] [PubMed]

2009 (6)

L. L. Ji, B. F. Shen, X. M. Zhang, F. C. Wang, Z. Y. Jin, C. Q. Xia, M. Wen, W. P. Wang, J. C. Xu, and M. Y. Yu, “Generating quasi-single-cycle relativistic laser pulses by laser-foil interaction,” Phys. Rev. Lett.103, 215005 (2009).
[CrossRef]

U. Teubner and P. Gibbon, “High-order harmonics from laser-irradiated plasma surfaces,” Rev. Mod. Phys.81, 445–479 (2009).
[CrossRef]

X. Q. Yan, H. C. Wu, Z. M. Sheng, J. E. Chen, and J. Meyer-ter Vehn, “Self-organizing gev, nanocoulomb, collimated proton beam from laser foil interaction at 7 × 1021W/cm2,” Phys. Rev. Lett.103, 135001 (2009).
[CrossRef]

A. Pukhov, T. Baeva, and D. an der Brgge, “Relativistic laser plasmas for novel radiation sources,” Eur. Phys. J. Spec. Top.175, 25–33 (2009).
[CrossRef]

T. Yu, M. Chen, and A. Pukhov, “High quality gev proton beams from a density-modulated foil target,” Laser Part. Beams27, 611–617 (2009).
[CrossRef]

M. Chen, A. Pukhov, T. P. Yu, and Z. M. Sheng, “Enhanced collimated gev monoenergetic ion acceleration from a shaped foil target irradiated by a circularly polarized laser pulse,” Phys. Rev. Lett.103, 024801 (2009).
[CrossRef] [PubMed]

2008 (4)

M. Chen, A. Pukhov, Z. M. Sheng, and X. Q. Yan, “Laser mode effects on the ion acceleration during circularly polarized laser pulse interaction with foil targets,” Phys. Plasmas15, 113103 (2008).
[CrossRef]

M. F. Kling and M. J. J. Vrakking, “Attosecond electron dynamics,” Annu. Rev. Phys. Chem.59, 463–492 (2008).
[CrossRef]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science320, 1614–1617 (2008).
[CrossRef] [PubMed]

T. J. M. Boyd and R. Ondarza-Rovira, “Anomalies in universal intensity scaling in ultrarelativistic laser-plasma interactions,” Phys. Rev. Lett.101, 125004 (2008).
[CrossRef] [PubMed]

2007 (3)

D. an der Brügge and A. Pukhov, “Propagation of relativistic surface harmonics radiation in free space,” Phys. Plasmas14, 093104 (2007).
[CrossRef]

M. Geissler, S. Rykovanov, J. Schreiber, J. M. ter Vehn, and G. D. Tsakiris, “3d simulations of surface harmonic generation with few-cycle laser pulses,” New J. Phys.9, 218 (2007).
[CrossRef]

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys.70, 1–87 (2007).
[CrossRef]

2006 (9)

T. Baeva, S. Gordienko, and A. Pukhov, “Theory of high-order harmonic generation in relativistic laser interaction with overdense plasma,” Phys. Rev. E74, 046404 (2006).
[CrossRef]

T. Baeva, S. Gordienko, and A. Pukhov, “Relativistic plasma control for single attosecond x-ray burst generation,” Phys. Rev. E74, 065401 (2006).
[CrossRef]

B. Dromey, M. Zepf, a. Gopal, K. Lancaster, M. S. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nature Phys.2, 456–459 (2006).
[CrossRef]

G. D. Tsakiris, K. Eidmann, J. Meyer-ter Vehn, and F. Krausz, “Route to intense single attosecond pulses,” New J. Phys.8, 19 (2006).
[CrossRef]

F. Quéré, C. Thaury, P. Monot, S. Dobosz, P. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett.96, 125004 (2006).
[CrossRef] [PubMed]

F. Remacle and R. D. Levine, “An electronic time scale in chemistry,” Proc. Natl. Acad. Sci. U.S.A.103, 6793–6798 (2006).
[CrossRef] [PubMed]

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science314, 443–446 (2006).
[CrossRef] [PubMed]

G. D. Tsakiris, K. Eidmann, J. M. ter Vehn, and F. Krausz, “Route to intense single attosecond pulses,” New J. Phys.8, 19 (2006).
[CrossRef]

J. Zheng, Z.-M. Sheng, J. Zhang, M. Chen, and Y.-Y. Ma, “Effects of laser intensities and target shapes on attosecond pulse generation from irradiated solid surfaces,” Chin. Phys. Lett.23, 377–380 (2006).
[CrossRef]

2005 (3)

A. Macchi, F. Cattani, T. V. Liseykina, and F. Cornolti, “Laser acceleration of ion bunches at the front surface of overdense plasmas,” Phys. Rev. Lett.94, 165003 (2005).
[CrossRef] [PubMed]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, “Coherent focusing of high harmonics: A new way towards the extreme intensities,” Phys. Rev. Lett.94, 103903 (2005).
[CrossRef] [PubMed]

S. Gordienko and A. Pukhov, “Scalings for ultrarelativistic laser plasmas and quasimonoenergetic electrons,” Phys. Plasmas12, 043109 (2005).
[CrossRef]

2004 (5)

C. Nieter and J. R. Cary, “Vorpal: a versatile plasma simulation code,” J. Comput. Phys.196, 448–473 (2004).
[CrossRef]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, “Relativistic doppler effect: Universal spectra and zeptosecond pulses,” Phys. Rev. Lett.93, 115002 (2004).
[CrossRef] [PubMed]

N. M. Naumova, J. A. Nees, I. V. Sokolov, B. Hou, and G. A. Mourou, “Relativistic generation of isolated attosecond pulses in a λ3 focal volume,” Phys. Rev. Lett.92, 063902 (2004).
[CrossRef]

N. M. Naumova, J. A. Nees, B. Hou, G. A. Mourou, and I. V. Sokolov, “Isolated attosecond pulses generated by relativistic effects in a wavelength-cubedfocal volume,” Opt. Lett.29, 778–780 (2004).
[CrossRef] [PubMed]

T. Esirkepov, M. Borghesi, S. V. Bulanov, G. Mourou, and T. Tajima, “Highly efficient relativistic-ion generation in the laser-piston regime,” Phys. Rev. Lett.92, 175003 (2004).
[CrossRef] [PubMed]

1996 (1)

R. Lichters, J. M. ter Vehn, and A. Pukhov, “Short-pulse laser harmonics from oscillating plasma surfaces driven at relativistic intensity,” Phys. Plasmas3, 3425–3437 (1996).
[CrossRef]

1994 (1)

S. V. Bulanov, N. M. Naumova, and F. Pegoraro, “Interaction of an ultrashort, relativistically strong laser pulse with an overdense plasma,” Phys. Plasmas1, 745–757 (1994).
[CrossRef]

1993 (1)

A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett.70, 774–777 (1993).
[CrossRef]

1992 (2)

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett.68, 3535–3538 (1992).
[CrossRef] [PubMed]

S. C. Wilks, W. L. Kruer, M. Tabak, and A. B. Langdon, “Absorption of ultra-intense laser pulses,” Phys. Rev. Lett.69, 1383–1386 (1992).
[CrossRef] [PubMed]

Altucci, C.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science314, 443–446 (2006).
[CrossRef] [PubMed]

an der Brgge, D.

A. Pukhov, T. Baeva, and D. an der Brgge, “Relativistic laser plasmas for novel radiation sources,” Eur. Phys. J. Spec. Top.175, 25–33 (2009).
[CrossRef]

an der Brügge, D.

D. an der Brügge, N. Kumar, A. Pukhov, and C. Rödel, “Influence of surface waves on plasma high-order harmonic generation,” Phys. Rev. Lett.108, 125002 (2012).
[CrossRef] [PubMed]

D. an der Brügge and A. Pukhov, “Propagation of relativistic surface harmonics radiation in free space,” Phys. Plasmas14, 093104 (2007).
[CrossRef]

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science320, 1614–1617 (2008).
[CrossRef] [PubMed]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science320, 1614–1617 (2008).
[CrossRef] [PubMed]

Audebert, P.

F. Quéré, C. Thaury, P. Monot, S. Dobosz, P. Martin, J.-P. Geindre, and P. Audebert, “Coherent wake emission of high-order harmonics from overdense plasmas,” Phys. Rev. Lett.96, 125004 (2006).
[CrossRef] [PubMed]

Avaldi, L.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science314, 443–446 (2006).
[CrossRef] [PubMed]

Baeva, T.

A. Pukhov, T. Baeva, and D. an der Brgge, “Relativistic laser plasmas for novel radiation sources,” Eur. Phys. J. Spec. Top.175, 25–33 (2009).
[CrossRef]

T. Baeva, S. Gordienko, and A. Pukhov, “Theory of high-order harmonic generation in relativistic laser interaction with overdense plasma,” Phys. Rev. E74, 046404 (2006).
[CrossRef]

T. Baeva, S. Gordienko, and A. Pukhov, “Relativistic plasma control for single attosecond x-ray burst generation,” Phys. Rev. E74, 065401 (2006).
[CrossRef]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, “Coherent focusing of high harmonics: A new way towards the extreme intensities,” Phys. Rev. Lett.94, 103903 (2005).
[CrossRef] [PubMed]

S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, “Relativistic doppler effect: Universal spectra and zeptosecond pulses,” Phys. Rev. Lett.93, 115002 (2004).
[CrossRef] [PubMed]

Baifei, S.

J. Liangliang, S. Baifei, Z. Xiaomei, W. Wenpeng, Y. Yahong, W. Xiaofeng, Y. Longqing, and S. Yin, “Plasma approach for generating ultra-intense single attosecond pulse,” Plasma Sci. Technol.14, 859–863 (2012).
[CrossRef]

Balcou, P.

A. L’Huillier and P. Balcou, “High-order harmonic generation in rare gases with a 1-ps 1053-nm laser,” Phys. Rev. Lett.70, 774–777 (1993).
[CrossRef]

Benedetti, E.

G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira, S. De Silvestri, and M. Nisoli, “Isolated single-cycle attosecond pulses,” Science314, 443–446 (2006).
[CrossRef] [PubMed]

Borghesi, M.

T. Esirkepov, M. Borghesi, S. V. Bulanov, G. Mourou, and T. Tajima, “Highly efficient relativistic-ion generation in the laser-piston regime,” Phys. Rev. Lett.92, 175003 (2004).
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T.-P. Yu, A. Pukhov, Z.-M. Sheng, F. Liu, and G. Shvets, “Bright betatronlike x rays from radiation pressure acceleration of a mass-limited foil target,” Phys. Rev. Lett.110, 045001 (2013).
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T.-P. Yu, A. Pukhov, G. Shvets, and M. Chen, “Stable laser-driven proton beam acceleration from a two-ion-species ultrathin foil,” Phys. Rev. Lett.105, 065002 (2010).
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L. Ji, B. Shen, X. Zhang, M. Wen, C. Xia, W. Wang, J. Xu, Y. Yu, M. Yu, and Z. Xu, “Ultra-intense single attosecond pulse generated from circularly polarized laser interacting with overdense plasma,” Phys. Plasmas18, 083104 (2011).
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Yu., Y. H.

L. L. Ji, B. F. Shen, D. X. Li, D. Wang, Y. X. Leng, X. M. Zhang, M. Wen, W. P. Wang, J. C. Xu, and Y. H. Yu., “Relativistic single-cycled short-wavelength laser pulse compressed from a chirped pulse induced by laser-foil interaction,” Phys. Rev. Lett.105, 025001 (2010).
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L. Ji, B. Shen, X. Zhang, M. Wen, C. Xia, W. Wang, J. Xu, Y. Yu, M. Yu, and Z. Xu, “Ultra-intense single attosecond pulse generated from circularly polarized laser interacting with overdense plasma,” Phys. Plasmas18, 083104 (2011).
[CrossRef]

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L. L. Ji, B. F. Shen, D. X. Li, D. Wang, Y. X. Leng, X. M. Zhang, M. Wen, W. P. Wang, J. C. Xu, and Y. H. Yu., “Relativistic single-cycled short-wavelength laser pulse compressed from a chirped pulse induced by laser-foil interaction,” Phys. Rev. Lett.105, 025001 (2010).
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L. L. Ji, B. F. Shen, X. M. Zhang, F. C. Wang, Z. Y. Jin, C. Q. Xia, M. Wen, W. P. Wang, J. C. Xu, and M. Y. Yu, “Generating quasi-single-cycle relativistic laser pulses by laser-foil interaction,” Phys. Rev. Lett.103, 215005 (2009).
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Zheng, J.

J. Zheng, Z.-M. Sheng, J. Zhang, M. Chen, and Y.-Y. Ma, “Effects of laser intensities and target shapes on attosecond pulse generation from irradiated solid surfaces,” Chin. Phys. Lett.23, 377–380 (2006).
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B. Dromey, M. Zepf, a. Gopal, K. Lancaster, M. S. Wei, K. Krushelnick, M. Tatarakis, N. Vakakis, S. Moustaizis, R. Kodama, M. Tampo, C. Stoeckl, R. Clarke, H. Habara, D. Neely, S. Karsch, and P. Norreys, “High harmonic generation in the relativistic limit,” Nature Phys.2, 456–459 (2006).
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[CrossRef]

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M. Chen, A. Pukhov, T. P. Yu, and Z. M. Sheng, “Enhanced collimated gev monoenergetic ion acceleration from a shaped foil target irradiated by a circularly polarized laser pulse,” Phys. Rev. Lett.103, 024801 (2009).
[CrossRef] [PubMed]

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T.-P. Yu, A. Pukhov, G. Shvets, and M. Chen, “Stable laser-driven proton beam acceleration from a two-ion-species ultrathin foil,” Phys. Rev. Lett.105, 065002 (2010).
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[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

(a) The spatial distribution of electrons in uniform density target case at t = 31T0. The red dotted line is calculated from the analytical model in section 4. (b) The snapshots of the electrostatic field Ex (red solid line) and the incident laser field Ey (blue dashed line) along y = 0 at t = 31T0.

Fig. 2
Fig. 2

Spatial distribution of the reflected laser field magnitude Ey at (a) t = 34T0, (b) t = 44T0 and (c) t = 54T0. Temporal profile of the filtered attosecond pulses at the tracing positions of (d) (22λ0, 0), (e) (16λ0, 0) and (f) (10λ0, 0). Notice the different scales on the x and y axis.

Fig. 3
Fig. 3

Layout of density-modulated foil target (DMFT). A CP laser pulse is incident on the foil target with a Gaussian plasma density distribution in the transverse (y direction). The transverse density profile of the DMFT (curved black line) is defined by rd. The maximal electron density is n0 = 8ncwhile the cut-off is ncutoff = 0.2n0.

Fig. 4
Fig. 4

2D PIC simulation results for the DMFT case. (a) Spatial distribution of the reflected laser field magnitude Ey (color palette) at t = 36T0, and the temporal electron density distribution (gray level) at t = 31T0. The red dotted line is calculated from the analytical model in Section 4. (b) Temporal profile of the generated as pulse after the ω ≤ 3ω0 frequency filtering. (c) The spectrum of the reflected light observed at (25μm, 0). The red dashed line is the power law predicted by the ROM model. (d) The full width at half maximum (upper panel) and the peak intensities (lower panel) of the APs after filtering out the fundamental and the diploid frequency along x = 25μm.

Fig. 5
Fig. 5

Schematic drawing of the interaction model. The few-cycle incident laser pulse (red solid line) acts on the left side (x1) of the moving compressed electron layer (blue line). The ions (black thick line) are fixed with an initial density ni. The electric field (red dash-dot line) has a linear profile both in the depletion region (x0 < x < x1) and in the compressed layer (x1 < x < x2).

Fig. 6
Fig. 6

Numerical results from the analytical model. (a) Spatial positions of the plasma boundary of the uniform density target (blue dotted line) and the DMFT (red solid line) at t = 3T0. (b) The displacement (blue solid) and speed −βx (red solid) of the on-axis electron surface layer.

Fig. 7
Fig. 7

Snapshots of the electron densities and filtered impulse intensities for the case of (a) rd = 3λ0 and (b) rd = 7λ0. The electron densities at the time of t = 31T0 are drawn with gray gradient. The red dotted lines are the positions of the plasma boundaries calculated from the analytical model. Numbers (1) and (2) in subgraph (a) indicate the two intense impulses in the reflected radiation. Notice that the intensities of the impulses are normalized to I0.

Fig. 8
Fig. 8

Filtered radiation intensity distributions at t = 42T0 with different pulse phases for the cases of rd = 3λ0 ((a)–(c)) and rd = 7λ0 ((d)–(f)).

Equations (7)

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n 0 ( y ) = max { n cutoff , n 0 × exp ( y 2 / r d 2 ) } ,
S ( y ) = n 0 ( y ) n c a 0 ( y ) = { const , | y | 6.4 λ 0 0.08 exp ( y 2 / r L 2 ) , | y | > 6.4 λ 0
F p ( x , y ) = 4 I ( t x / c , y ) c σ ( x , y ) c u c + u ,
E ( x , y , t ) = E 0 sin 2 [ π ( t x / c ) 2 τ 0 ] e ( y r L ) 2 ,
d p d t = F p ( x , y ) e E x 0 ( x , y ) ,
d d t ( u c 2 u 2 ) = 4 π 2 [ 2 E 0 2 ( x , y , t ) c u c + u ( x 2 + 1 π 2 n e x ) n e x ] ,
S ( y ) = n 0 a 0 exp [ ( y r l ) 2 ( y r d ) 2 ] ,

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